There is nothing special about the moment you call motionless - it is motionless when looking from your frame of reference - but the ball "does not know" about that.
That means the moment is just like any other moment where it has some specific velocity v - just that v = 0 from your frame of reference.
But looking from an escalator nearby, that may be a different moment.
All the ball sees is an acceleration. We call it "Gravity of Earth" - but the ball does not know earth.
If we ignore Earth too, it gets much simpler: There is a start velocity, and an acceleration.
Whether the ball goes up, down, or is turning around all depends on from where you look.
So the moment we see the ball motionless is the instant the ball has velocity 0 relative to our frame of reference, while it is accelerated - so it does not keep this velocity, it "passes through" it.
But: Why does it look to us like the ball is motionless for a moment?
The brain is trained to recognize moving objects - we learned during evolution to react quickly to an unexpected object even at the edge of our field of view (to take care if it wants to eat us, etc).
Also, the system of eye and brain has evolved to allow us to see very fine details when nothing moves - this involves lots of processes in the brain - a lot more than just the eye itself.
The relevant point here is that these functions of the brain are different with not much in common.
When observing the ball, we watch a moving object, using one part of our brain, and when the relative velocity approaches 0, we switch to a different way of seeing, done in a different part of the brain. Then we switch back.
I assume the perceived moment of motionlessness caused by this process of switching, and specifically on the time it takes to decide when to switch back to "movement".